demerit vs lack

demerit

noun
  • A quality of being inadequate; a fault; a disadvantage 

  • A mark given for bad conduct to a person attending an educational institution or serving in the army. 

  • That which one merits or deserves, either of good or ill; desert. 

lack

noun
  • A deficiency or need (of something desirable or necessary); an absence, want. 

verb
  • To be short (of or for something). 

  • To be without, not to have, to need, to require. 

How often have the words demerit and lack occurred in a corpus of books? (source: Google Ngram Viewer )